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Constraint-First Reasoning: A Training-Free Protocol for Exploiting Answer-Space Constraints in Mathematical Problem Solving — arXiv:2608.05254

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.05254
License (as archived): CC0-1.0
Archived: 2026-10-25T21:27:06.340Z
SHA-256 of the archived text: 8e2360ec0f0eabc65a79e4b49036105ccfbce37f0f809f85a8f97733323654b4
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How to cite

Constraint-First Reasoning: A Training-Free Protocol for Exploiting Answer-Space Constraints in Mathematical Problem Solving — arXiv:2608.05254 — arXiv (en), https://arxiv.org/abs/2608.05254 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_10303bf4cdae (Metraipolis archive dc_10303bf4cdae, sha256 8e2360ec0f0eabc65a79e4b49036105ccfbce37f0f809f85a8f97733323654b4)

BibTeX

@misc{dc10303bf4cdae,
  title = {Constraint-First Reasoning: A Training-Free Protocol for Exploiting Answer-Space Constraints in Mathematical Problem Solving — arXiv:2608.05254},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.05254},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_10303bf4cdae; sha256 8e2360ec0f0eabc65a79e4b49036105ccfbce37f0f809f85a8f97733323654b4},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.05254. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Large language models can derive a plausible mathematical object yet still violate explicit requirements--for example, by omitting a modular reduction, returning a non-integer, or using the wrong encoded answer form. We introduce Constraint-First Reasoning (CFR), a training-free two-stage prompting protocol: Stage 1 extracts and summarizes constraints entailed by the problem, and Stage 2 solves while checking intermediate and final results against that summary. Routed-CFR activates the two-stage protocol only when a text-only regex router detects restrictive cues; otherwise it uses direct chain-of-thought (CoT). Across AIME, CMIMC, BRUMO, and AIMO_AMC, the method improves direct CoT on multiple backbones. We further report convention-controlled routing experiments, matched prompting baselines, problem-level paired tests, decoding robustness, constraint-quality audits, total-token accounting, and an OlympiadBench evaluation. These analyses position CFR as a targeted test-time intervention whose benefit depends on recoverable constraints and reliable Stage 1 extraction, rather than as a general-purpose replacement for mathematical reasoning.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-07 in cs.CL).
Categorie arXiv: Computation and Language (cs.CL) ; Symbolic Computation (cs.SC).
Pagina del lavoro: https://arxiv.org/abs/2608.05254 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-25T21:24:38.186Z dalla pagina https://arxiv.org/catchup/cs.CL/2026-08-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).